1. Field of the Invention
The present invention relates to an exposure method, and particularly, to an exposure method used to form a daughter mask from a master mask or to form a semiconductor device having precision patterns.
2. Description of the Related Art
A step-and-repeat exposure method moves a stage of an exposure apparatus on which a substrate is set by a predetermined distance whenever makes a shot of exposure on the substrate through a mask. By repeating the stage-moving and exposing processes, the method forms patterns on the substrate from the mask.
This method never considers positional linear errors including scaling and orthogonality errors related to the mask, an optical system of the exposure apparatus, and the stage of the exposure apparatus. There is, indeed, no need of considering such linear errors when forming a pattern on a new substrate by exposure, or it is only required to control overlapping correctness when forming a pattern on another pattern on a substrate. Namely, the prior art controls positional errors of a pattern only on a coordinate system defined on the substrate. To correctly form patterns on a substrate, it is necessary to control positional errors of the patterns not only on the coordinate system defined on the substrate but also on a coordinate system on which the stage is moved.
Recent technology uses master masks having different patterns to form an integrated pattern on a substrate by successively exposing the substrate through the master masks, so that the exposed substrate may be used as a daughter mask.
FIG. 10 shows examples of such master and daughter masks. Master masks I to VI have different patterns and are used one after another to expose a substrate by an exposure apparatus and form an integrated pattern on the substrate serving as the daughter mask. At this time, boundaries of the six exposure shot areas on the substrate must align with one another. To achieve this, it is necessary to precisely control not only positional errors of the shot areas on a coordinate system defined on a stage of the exposure apparatus but also positional errors thereof on a coordinate system on which the stage is moved.
Under ideal exposure conditions involving no linear errors, the boundaries of exposure shot areas on a substrate align with one another and cross patterns in the exposure shot areas are on rectangular coordinates, as shown in FIG. 11.
In practice, the boundaries of shot areas on a substrate separate from one another as shown in FIG. 12. This is because a coordinate system defined on a stage of an exposure apparatus on which the substrate is set is misaligned with a coordinate system on which the stage is moved. In this case, cross patterns in the exposure shot areas deviate from rectangular coordinates.
Positional errors of patterns on a substrate are frequently very large and nonlinear because they are an accumulation of mask and apparatus errors.
The conventional exposure method is unable to solve these errors, and therefore, is incapable of forming precision patterns on a substrate.
An object of the present invention is to provide an exposure method capable of precisely adjusting the positions of patterns on a substrate.
In order to accomplish the object, the present invention provides a method of repeatedly exposing a substrate, which is set on a stage of an exposure apparatus, through at least one mask to form patterns on the substrate. The method includes the steps of finding first positional linear errors of a pattern to be formed by the mask on a first coordinate system defined on the substrate and second positional linear errors of the pattern on a second coordinate system on which the stage is moved, and correcting a scaling factor of the exposure apparatus, or coordinates for moving the stage on the second coordinate system, or both, to equalize the first and second linear errors to each other.
The first aspect eliminates the difference between the first and second positional linear errors. As a result, a complex of the first and second positional linear errors is also linear and is removable to leave only random residual errors. Consequently, the first aspect is capable of precisely forming patterns on a substrate by exposure through masks.
A second aspect of the present invention provides a method of repeatedly exposing a substrate, which is set on a stage of an exposure apparatus whose optical scaling factor is adjustable, through a mask to form patterns on the substrate. The method includes the steps of finding, according to positional linear error components specific to the mask and positional linear error components specific to the exposure apparatus, first linear errors of a pattern to be formed by the mask on a first coordinate system defined on the substrate, finding second linear errors as differences between the first linear errors and linear errors specific to the stage, and correcting, according to the second linear errors, coordinates for moving the stage on a second coordinate system.
The second aspect eliminates the difference between the first and second coordinate systems. As a result, only linear errors that are removable remain. The second aspect grasps linear errors specific to the exposure apparatus and corrects coordinates for moving the stage on the second coordinate system without actually forming a sample pattern on a substrate and measuring the same whenever a mask is replaced.
A third aspect of the present invention provides a method of repeatedly exposing a substrate, which is set on a stage of an exposure apparatus, through a plurality of masks to form patterns on the substrate. The method includes the steps of calculating, for each mask, the average of X- and Y-scale errors specific to the mask, adjusting a scaling factor of the exposure apparatus to equalize the X-Y-scale-error averages of the masks to one another, calculating linear-error averages of the masks after the scaling factor correction, using the linear-error averages as representative positional linear errors of each mask, calculating linear errors of a pattern to be formed by a given mask on a first coordinate system defined on the substrate according to the representative positional linear errors and positional linear errors specific to the exposure apparatus.
The third aspect considerably reduces the difference between the positional linear errors of a pattern to be formed by the mask on the first coordinate system defined on the substrate and the positional linear errors of the pattern on the second coordinate system.
A fourth aspect of the present invention provides a method of repeatedly exposing a substrate, which is set on a stage of an exposure apparatus whose linear errors are separately adjustable, through a plurality of masks to form patterns on the substrate. The method includes the step of equalizing, for each mask, first linear error components of a pattern to be formed by the masks on a first coordinate system defined on the substrate to second linear error components on a second coordinate system on which the stage is moved.
The fourth aspect eliminates the difference between the positional linear errors on the first coordinate system defined on the substrate and the positional linear errors on the second coordinate system.